AP Stat Homework- Answers to Chapter 2 excersises

2.8 (p.106)

Two mothers are 57 inches tall; their husbands are 66 and 67 inches tall.(b)The two tallest fathers are 74 inches tall; there are three of them and their wives are 62, 64, and 67 inches tall. (c) Their is no clear explainory variable, so either axis is fine. (d) The weak positive association indicate that people have some tendancy to marry persons of similar height, but it is not overwhelming. It is weak since there is a great deal of scatter.

2.10 (p.108) (b) Positive association; approx. linear except for the two outliers at 160 actual calories that are guessed over 360, the spaghetti and the snack cake.

2.17 (p.113) With x as femur length and y as humerus length, x-bar = 58.2, sx = 13.2 y-bar = 66.0 and sy = 15.89; r = 0.994

2.18 (p.116) Because there is no obvious linear relationship, one expects the correlation to be near zero.

2.24 (p.118) r= 0.82450, a positive association. it is not close to 1 because of the outliers. (b) It has no effect on the correlation. If every guess had been 100 calories higher, the correlation would be exactly the same, since to compute correlation each score is standardized according to the mean and standard deviation of the x and y variables. (c) without the outliers, the correlation is higher r= 0.98374

2.25 (p.118) (c) r= 0.25310 for both sets of data. For the first set, the x values range from -4 to 4, a spread of 8 units while the spread of the y scores are 1.1 units. For the second set of data, the horizontal spread is small, only 0.8 units, compared to the vertical spread of 11 units. What matters in computing the correlation isn't the actual sizes of the spreads in each direction, but rather the relative sizes of these spreads, which is more difficult to see unless we make to separate plots, each with appropriate x and y scales.

2.28 (p.119) (a) Sex is a categorical variable (b) r must be between -1 and +1 (c) r should have no units ( so 0.23 bushels is wrong)

2.29 (p.123) a = 1.0892 and b= 0.1890 as given (b) x-bar = 22.31, sx = 17.74; y-bar = 5.306, sy = 3.368; r = 0.99526. Except for round off error we again find b= 0.1890 and a= 1.0892

2.31 (p.124) (b) The slope is close to 1, so the strength after 28 days is approximately (strength are one week) plus 1389 psi. In other words, we expect the extra three weeks to add about 1400 psi of strength to the concrete. (c) 4557 psi.

2.33 (p.128) (b) there is a very strong positive linear relationship. r= 0.9990. (c) regression line y-hat = 1.76608 +0.080284x (y is steps/second, x is speed). (d) r²= 0.998, so nearly all the variation (99.8% of it)in steps taken per second is explained by the linear relationship. (e) The regression line would be different (See Example 2.11 on page 125). the line in part c of this question is based on minimizing the sum of the squared vertical distances on the graph. This new regression would minimize the squared horizontal distances. r², however would remain the same, however.

2.35 (p.136) (b) the line is clearly not a good predictor on the actual data. (c) the sum is -0.01 which is a reasonable discrepancy allowing for round off error.

2.36 (p.136)let y be "guessed calories" and x be actual calories. Using all points: y-hat = 58.59 + 1.3036x and r² = 0.68. Excluding the spaghetti and the snack cake we have y-hat = 43.88 + 1.14721x and r² = 0.968! (c) The two removed points could be called influential since when they are included, the regression line passes above all the other points.

2.42 (p.139) (b) r = 0.56896 and r²= 0.32372. There is a moderate positive association between US and overseas stock returns. This relations ship explains around 32% of the variation. (c) y-hat = 4.777 + 0.8130x (d) y-hat = 12% We can explain only about one third of the variation of overseas returns with the US return information, as evidenced by the wide scatter around the line, so we should not expect too much accuracy in our predictions. (e) the outlier point occured in 1986. 1973 and 1974 are potentially influential.

2.43 (p.140) when x= 480, y-hat = 255.95 cm or 100.77 in., or about 8.4 feet!

2.46 (p.141) r₁ = 0.81642, y-hat₁ = 3.000 + 5.001x. r₂ = 0.81624, y-hat₂ = 3.001 + 5.000x. r₃ = 0.81652, y-hat₃ = 3.002 + 4.999x. (c) The regression line looks reasonable for the first data set , though with a lot of scatter. The second is definitely non-linear. x=14 is quite far from the mark. The third data set x=19 is influential. We have little confidence in the estimate when x=14.

2.47 (p.143) y-hat = 1166.93 - 0.58679 x. (b) Based on the slope, the farm populations decreased about 590,000 people per year. The regression line explains about 97.7 % of the variation (c) -782,100 people (which is a silly answer).

2.48 (p.145) Explainitory variable: Consumption of Herbal Tea" and the response variable is "Cheerfulness" Lurking variable: social interaction.

2.50 (p.148) Lurking variable: the seriousness of the fire. A large fire summons more fire fighters.

2.55 (p.149) The explainitory variable is whether or not a student has taken at least 2 years of foreign language, and the score on the test is the response. The lurking variable is the students English skills before taking (or not taking) the foreign language: students who have a good command of English early in their high school career are more likely to choose (or be advised to choose) to take a foreign language.

2.60 (p.152) (a) 5375. (b) 1004 / 5375 = 18.7% (c) Both parents smoke: 1780 (33.1%); One parent smokes: 2239 (41.7%); Neither parent smokes: 1356 (25.2%).

2.65 (p.156) Two possible answers: Row 1-30, 20; Row 2-30, 20; and Row 1-10, 40; Row 2-50,0.

2.66 (p.156) (a) 6014; 1.26% (b) Blood pressure is explanatory (c) Yes; among those with low blood pressure, 0.785% died; the death rate in the high blood pressure group was 1.65% (about twice as high as the other group).

2.68 (p.160)

	Admit	Deny
Male	490	210
Female	280	220

(b) 70% of male applicants are admitted, while only 56% of females are admitted. (c) 80% of male business school applicants are admitted, compared with 90% of females; in the law school, 10% of males are admitted , compared with 33% of females. (d) Six out of Seven men apply to the business school, which admits 83% of all applicants, while 3 of 5 women apply to the law school which only admits 27&.5 of its applicants.

2.70 (p.160)

	Hit	No Hit
All pitchers
Joe	120	380
Moe	130	370
Right-Handed
Joe	40	60
Moe	120	280
South Paw
Joe	80	320
Moe	10	90

(b) Joe .240, Moe: .260 Moe has the best overall average (c) Against right handed pitchers: Joe: .400, Moe: .300. Against left handed pitchers: Joe: .200, Moe: .100. Joe is better against both kinds of pitchers. (d) Both players do better against right handed pitchers than against left handed pitchers. Joe spent 80% of his at-bats facing lefties, while Moe only faced left handers 20% of the time.